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A heap of paddy is in the form of a
right circular cone whose diameter
is 4.2 m and height 2.8 m. If the heap
is to be covered exactly by a canvas
to protect it from rain then find
the area of the canvas needed.

r = 4.2/2 = 2.1 m
h = 2.8 m
slant height l = sqrt[r^2 +h^2]
=sqrt[2.1^2 +2.8^2]
= sqrt[4.41+7.84]=sqrt[12.25]=3.5m
Curved surface area of a cone
= pi * r*l
=[22/7]*2.1*3.5
=23.1 sq.m.
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problem2
A tent is in the shape of a right circular cylinder  surmounted
 by a cone. The total height and
diameter of the base are 13.5 m
and 28 m. If the height  of the
cylindrical portion is 3 m , find
the total surface area of the tent.

Draw a diagram
Cylinder:
r = 28/2 = 14 m
h=3m
Cone :
r = 14 m (note that only the radii
of the cone and cylinder are the same)
height is different
, so use another notation
H = 13.5 -3 = 10.5 m
r=sqrt[r^2 + H^2]
=sqrt[14^2 + 10.5^2]
=sqrt[196+110.25]
=sqrt[306.25]=17.5m
Total area  =  CSA of cylinder + CSA
of cone
=2*pi*r*h+pi*r*l
=pi*r*[2*h + l ]
=(22/7)*14*[2*3+17.5]
=(22/7)*14*[23.5]
=1034 sq.m.



other questions and problems:


*integral calculus integration formula





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trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
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